Question: Simplify the following expression: $ t = -1 + \dfrac{-7r + 2}{9r + 6} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9r + 6}{9r + 6}$ $ \dfrac{-1}{1} \times \dfrac{9r + 6}{9r + 6} = \dfrac{-9r - 6}{9r + 6} $ Therefore $ t = \dfrac{-9r - 6}{9r + 6} + \dfrac{-7r + 2}{9r + 6} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-9r - 6 - 7r + 2}{9r + 6} $ $t = \dfrac{-16r - 4}{9r + 6}$